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Category: Integration

find-D-x-4-y-4-dxdy-with-D-x-y-R-2-1-lt-x-2-y-2-lt-2-1-lt-xy-lt-2-x-gt-0-y-gt-0-

Question Number 31086 by abdo imad last updated on 02/Mar/18 $${find}\:\int\int_{{D}} \left({x}^{\mathrm{4}} \:−{y}^{\mathrm{4}} \right){dxdy}\:{with} \\ $$$${D}=\:\left\{\left({x},{y}\right)\in{R}^{\mathrm{2}} /\:\mathrm{1}<{x}^{\mathrm{2}} \:−{y}^{\mathrm{2}} <\mathrm{2}\:,\mathrm{1}<{xy}<\mathrm{2}\:,{x}>\mathrm{0},{y}>\mathrm{0}\right\} \\ $$ Terms of Service Privacy…

calculate-by-two-methods-0-1-0-pi-2-dx-dt-1-x-2-tan-2-t-then-find-the-value-of-0-pi-2-t-cotant-dt-

Question Number 31083 by abdo imad last updated on 02/Mar/18 $${calculate}\:{by}\:{two}\:{methods}\:\int_{\mathrm{0}} ^{\mathrm{1}} \:\:\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \:\:\:\frac{{dx}\:{dt}}{\mathrm{1}+{x}^{\mathrm{2}} {tan}^{\mathrm{2}} {t}} \\ $$$${then}\:{find}\:{the}\:{value}\:{of}\:\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \:{t}\:{cotant}\:{dt}\:. \\ $$$$ \\ $$…

find-D-dxdy-x-y-4-with-D-x-y-R-2-x-1-y-1-x-y-4-

Question Number 31084 by abdo imad last updated on 02/Mar/18 $${find}\:\int\int_{{D}} \:\:\frac{{dxdy}}{\left({x}+{y}\right)^{\mathrm{4}} }\:\:{with}\:{D}=\left\{\left({x},{y}\right)\in{R}^{\mathrm{2}} /{x}\geqslant\mathrm{1},{y}\geqslant\mathrm{1},{x}+{y}\leqslant\mathrm{4}\right\} \\ $$ Commented by abdo imad last updated on 11/Mar/18 $${x}+{y}\:\leqslant\mathrm{4}\:\:{and}\:{y}\geqslant\mathrm{1}\:\Rightarrow−{y}\leqslant−\mathrm{1}\:{but}\:{x}\:\leqslant\mathrm{4}−{y}\:\Rightarrow\mathrm{1}\leqslant{x}\leqslant\mathrm{3}\:{and}…

calculate-by-two-methods-0-0-dxdy-1-y-1-x-2-y-then-find-the-value-of-0-lnx-1-x-2-dx-

Question Number 31082 by abdo imad last updated on 02/Mar/18 $${calculate}\:{by}\:{two}\:{methods}\:\int_{\mathrm{0}} ^{\infty} \int_{\mathrm{0}} ^{\infty} \:\:\:\frac{{dxdy}}{\left(\mathrm{1}+{y}\right)\left(\mathrm{1}+{x}^{\mathrm{2}} {y}\right)} \\ $$$${then}\:{find}\:{the}\:{value}\:{of}\:\int_{\mathrm{0}} ^{\infty} \:\frac{{lnx}}{\mathrm{1}−{x}^{\mathrm{2}} }{dx}. \\ $$ Terms of…